Base field \(\Q(\sqrt{417}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 104\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[6,6,w + 10]$ |
| Dimension: | $17$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $56$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{17} + x^{16} - 28x^{15} - 28x^{14} + 317x^{13} + 312x^{12} - 1873x^{11} - 1777x^{10} + 6220x^{9} + 5560x^{8} - 11573x^{7} - 9623x^{6} + 10966x^{5} + 8723x^{4} - 3662x^{3} - 3388x^{2} - 416x + 12\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, 107w - 1146]$ | $-1$ |
| 2 | $[2, 2, 107w + 1039]$ | $\phantom{-}e$ |
| 3 | $[3, 3, 1108w - 11867]$ | $-1$ |
| 7 | $[7, 7, 38w - 407]$ | $...$ |
| 7 | $[7, 7, -38w - 369]$ | $...$ |
| 13 | $[13, 13, -4w - 39]$ | $...$ |
| 13 | $[13, 13, 4w - 43]$ | $...$ |
| 17 | $[17, 17, 2w + 19]$ | $...$ |
| 17 | $[17, 17, -2w + 21]$ | $...$ |
| 23 | $[23, 23, -24w - 233]$ | $...$ |
| 23 | $[23, 23, 24w - 257]$ | $...$ |
| 25 | $[25, 5, -5]$ | $...$ |
| 31 | $[31, 31, -894w - 8681]$ | $...$ |
| 31 | $[31, 31, -894w + 9575]$ | $...$ |
| 37 | $[37, 37, 252w - 2699]$ | $...$ |
| 37 | $[37, 37, 252w + 2447]$ | $...$ |
| 53 | $[53, 53, -1322w - 12837]$ | $...$ |
| 53 | $[53, 53, 1322w - 14159]$ | $...$ |
| 59 | $[59, 59, -100w - 971]$ | $...$ |
| 59 | $[59, 59, 100w - 1071]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2,2,-107w + 1146]$ | $1$ |
| $3$ | $[3,3,-1108w - 10759]$ | $1$ |